A considerable amount of equipment has only two available operating states: on and off. Examples include pumps, compressors, grinders, computer servers, and many others. This equipment is used to meet an operational need, often multiple needs. Finding a schedule to meet even a single operational need at lowest cost is not easy because the number of possible schedules may be exponentially large.
For example, an hourly schedule covering one day for one piece of equipment has 224 or about 1.7 million possibilities. The problem becomes even more difficult when multiple operating needs or objectives are considered.
Current operating schedules for equipment are mostly developed by manual analysis, or intuition-based on experience. In a minority of cases, computer aided decision support systems may provide a schedule based on a single objective or goal.
Approaches proposed in the current literature for multi-objective scheduling problem mainly fall into two categories: optimization techniques and meta-heuristics.
Optimization approaches utilize linear, nonlinear, dynamic, mixed, and integer programming to find the schedule that minimizes a single deterministic objective function related to the energy costs.
The pump scheduling optimization problem is complex as it involves a set of non-linear constraints and a set of binary decision variables. In order to make the problem tractable, simplifications are usually made through assumptions, discretization, or heuristic rules.
While sophisticated search and optimization techniques to solve this problem have been proposed, actual applications of such approaches have generally been restricted to few case studies because such approaches greatly simplify the complexities and interdependencies of real pumped fluid (e.g., water) distribution networks.
Hybrid optimization methods have been developed that combines linear programming (LP) with a local search strategy. In the first stage, an optimization model is run on the basis of the linearization of the entire water-distribution model. The second stage of the optimization involves the application of a local search algorithm which proved to be efficient in finding a local optimum by exploring the neighborhood of a solution for improvements.
Metaheuristics such as genetic algorithms and simulated annealing have also been used to tackle the multi-objective scheduling problems. Mainly, in water networks metaheuristics are coupled with a simulator to capture properties of the system. These approaches have been known to be effective in solving pump scheduling problems. Although such approaches do not require simplifications of the hydraulic model which makes them more powerful alternatives to classic optimization techniques however they still suffer from a fundamental drawback as they do not guarantee to find the optimal pump schedule. Additionally, metaheuristics may require a large number of simulation runs which is computationally expensive.